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Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this paper, the similarity representation of the original system of partial differentiation equations is formulated as a system of nonlinear ordinary differential equations with auxiliary conditions, and closed form solutions are obtained for a linear rod, for a nonlinear rod subjected to constant velocity impact and a weekly non-linear rod.
1 citations
27 Jan 2010
TL;DR: In this article, boundary layer similarity flow of a non-Newtonian power law fluid past an impermeable flat plate, driven by a power law velocity profile U = Byσ, is considered.
Abstract: In this paper we consider boundary layer similarity flow of a non-Newtonian power law fluid past an impermeable flat plate, driven by a power law velocity profile U = Byσ. We show that the momentum equation has power series solutions, valid for all the allowed range of the parameter σ.
1 citations
TL;DR: In this paper, the Navier-Stokes equations governing the flow, are reduced to a third-order ordinary differential equation of a boundary value problem with a semi-infinite domain by using similarity transformation.
Abstract: In this study, we propose an efficient and accurate numerical technique that is called the rational Chebyshev collocation (RCC) method to solve the two dimensional flow of a viscous fluid in the vicinity of a stagnation point named Hiemenz flow The Navier-Stokes equations governing the flow, are reduced to a third-order ordinary differential equation of a boundary value problem with a semi-infinite domain by using similarity transformation The rational Chebyshev method reduces this nonlinear ordinary differential equation to a system of algebraic equations This technique is a powerful type of the collocation methods for solving the boundary value problems over a semi-infinite interval without truncating it to a finite domain We also present the comparison of this work with others and show that the present method is more accurate and efficient
1 citations
TL;DR: In this paper, the nonlinear, partial differential equations describing the compressible flow of a viscous and heat conducting gas in a cone are reduced to two coupled, ordinary, nonlinear differential equations by means of a self-similar transformation.
Abstract: The nonlinear, partial differential equations describing the compressible flow of a viscous and heat conducting gas in a cone are reduced to two coupled, ordinary, nonlinear differential equations by means of a self‐similar transformation. These are solved numerically for the velocity and temperature distributions in the cone. It is shown that for given flow numbers R, P, and M, laminar flows exist only up to a critical cone angle ϑ0.
1 citations